Probabilistic representations of fragmentation equations

Abstract

In this survey article, we present an overview of a large class of probabilistic representations of the fragmentation equation, and we develop and study the interconnections in between these representations. We focus on the stochastic process which represents the evolution of the mass of a typical particle which undergoes fragmentation in time. These probabilistic representations range from Markov chains to stochastic differential equations with jumps, and we aim at constructing how they are inter-related. In particular, we show how these representations can be used to develop easy to implement numerical methods.